Method and program for calculating exposure dose and focus position in exposure apparatus, and device manufacturing method

ABSTRACT

A method for calculating an offset of an exposure dose and a focus position in an exposure apparatus that exposes a substrate via an original includes the steps of obtaining information of a shape of a pattern formed on the substrate using the exposure apparatus, calculating a shift amount between a critical dimension contained in the information of the shape of the pattern and a reference value of the critical dimension, and calculating an offset of the focus position based on the information of the shape of the pattern, and calculating the offset of the exposure dose based on the shift amount and the offset of the focus position.

BACKGROUND OF THE INVENTION

The present invention relates generally to a technology of calculatingan exposure dose and a focus position in an exposure apparatus.

The pattern exposure technology that transfers an LSI pattern on areticle onto a wafer is required to improve the productivity as well aspromoting the fine processing to a transferable pattern. The exposureprocess in the exposure apparatus sets an optimal value of an exposurecondition, such as a focus position and an exposure dose, for eachprocess and for each exposure layer, in exposing the wafer.

The optimal exposure condition, such as the focus position and theexposure dose, is set as a result of that a shape measurement apparatus,such as a critical dimension scanning electron microscope (“CD-SEM”)measures a predetermined resist pattern shape. An etched pattern shapeis also measured, and both shapes are compared. However, various errors,such as the resist's refractive index and thickness, exposure controland focusing of the exposure apparatus, a development time period, adeveloper's characteristic, an uneven hot plate, a PEB temperature andtime period, and a reticle manufacturing error (flatness), differentiatetheir measurement values, cause a CD error, and lower a manufacturingyield rate. One proposed method calculates and controls the exposuredose using a means for setting a resist's refractive index andthickness. See, for example, Japanese Patent Application, PublicationNo. 62-132318. Another proposal improves the wafer's CD error byadjusting the exposure dose against the reticle error. See, for example,Japanese Patent Application, Publication No. 10-032160. When the CDfluctuates approximately concentrically to the wafer, still anotherproposal prepares a function between a distance from a wafer's centerand the exposure dose, and controls the exposure dose for each shot.See, for example, Japanese Patent Application, Publication No.10-064801. Yet another proposed method prepares an exposure dose map foreach shot from CD measurement values of the exposed whole wafer planeand exposed whole shot plane, and controls the exposure dose inaccordance with the map. See, for example, Japanese Patent Application,Publication No. 2005-094015.

The fine-processing demand gradually increases a numerical aperture(“NA”) of a projection optical system in the exposure apparatus, andgradually decreases a depth of focus (“DOF”). For example, the DOF forthe 90 nm CD pattern is merely about 200 nm with 10% latitude for the CDfluctuation.

A method of setting the exposure condition for the narrow DOF isrequired to change a focus position to an exposure dose window (“EDwindow”) as well as control over a CD value through a change of anexposure dose.

Japanese Patent Applications, Publication Nos. 62-132318, 10-032160,10-064801, and 2005-094015 propose methods of setting an exposure dosesuitable for each of various errors, but are silent about an effectivecontrol method of controlling a focusing position. This is because noprior art provide exposures with minutely changed focus positions unlikea focus exposure matrix (FEM) pattern, or an approach that calculate ashift amount of a focus position from one exposure condition. One reasonrests in use of a CD-SEM for a CD measurement. The CD measurement fromone mark provides only one measurement result of a CD value, and onlyone variable can be varied. Therefore, Japanese Patent Applications,Publication Nos. 62-132318, 10-032160, 10-064801, and 2005-094015 haslimits to the transferable pattern. Accordingly, one proposed methodcalculates an offset of an exposure dose and an offset of a focusposition (substrate position) in the exposure apparatus. See, forexample, Japanese Patent Application, Publication No. 2003-142397, whichcreates a library of a correlation among the offsets of the exposuredose and the focus position (substrate position) and a light intensitysignal waveform of a pattern, and measures the light intensity signalwaveform of the pattern obtained for a certain exposure dose and focusposition. Thereafter, this reference calculates the offsets of theexposure dose and the focus position based on the library and themeasured light intensity signal waveform.

Nevertheless, the previously prepared library does not conform to thestatus quo in the method of Japanese Patent Application, Publication No.2003-142397 as an extrinsic factor that affects the CD fluctuates, suchas the resist's refractive index and thickness, exposure control andfocusing in the exposure apparatus, a development time period, adeveloper's characteristic, an uneven hot plate, a PEB temperature andtime period, and a reticle manufacturing error (flatness). Then, thismethod needs to properly update the library.

SUMMARY OF THE INVENTION

The present invention is directed to a technology that calculates theoffsets of the exposure dose and the focus position, and is less likelyto be affected by the extrinsic factor or a fluctuation of thelithography environment.

A method according to one aspect of the present invention forcalculating an offset of an exposure dose and a focus position in anexposure apparatus that exposes a substrate via an original includes thesteps of obtaining information of a shape of a pattern formed on thesubstrate using the exposure apparatus, calculating a shift amountbetween a reference value of a critical dimension and the criticaldimension contained in the information of the shape of the pattern, andcalculating an offset of the focus position based on the information ofthe shape of the pattern, and calculating the offset of the exposuredose based on the shift amount and the offset of the focus position.

Other objects and further features of the present invention will becomereadily apparent from the following description of the preferredembodiments with reference to accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate embodiments of the invention and,together with the description, serve to explain the principles of theinvention.

FIG. 1 is a schematic block diagram of a semiconductor manufacturingsystem according to one embodiment.

FIG. 2 is a schematic block diagram of a structure of an exposureapparatus shown in FIG. 1.

FIG. 3 is a flowchart showing an exposure method of the exposureapparatus shown in FIG. 2.

FIG. 4 is a flowchart of an FEM pattern manufacturing method in theflowchart shown in FIG. 3.

FIG. 5 is image data showing a measurement result using a normal CD-SEM.

FIG. 6 is image data showing a measurement result obtained from anobservation of a wafer shown in FIG. 5 that is inclined by 15°.

FIG. 7 is a graph that converts the image data shown in FIGS. 5 and 6into shape information.

FIG. 8 is an enlarged view of part of a resist pattern in each shot ofthe FEM pattern formed on the wafer.

FIG. 9 is a graph obtained through a measurement of a CD, a height, anda sidewall angle in a three-dimensional shape of the resist patternshown in FIG. 8.

FIG. 10 is an enlarged view of part of a resist pattern in each shot ofthe FEM pattern formed on the wafer.

FIG. 11 is a graph showing a relationship between a CD and the exposuredose obtained from a pattern in a thick frame of the resist patternshown in FIG. 10.

FIG. 12 is an enlarged view of part of a resist pattern in each shot ofthe FEM pattern formed on the wafer.

FIG. 13 is a graph showing a relationship between a CD and the exposuredose obtained from a pattern in a thick frame of the resist patternshown in FIG. 12.

FIG. 14 is a graph showing the offsets from the optimal exposure doseand the optimal focus position in each shot of the FEM pattern formed onthe wafer.

FIG. 15 is a flowchart used to calculate the offsets of the focusposition and the exposure dose using the shape measurement value.

FIG. 16 is a flowchart of a device manufacturing method using theexposure apparatus shown in FIG. 2.

FIG. 17 is a detailed flowchart for Step 4 shown in FIG. 16.

FIG. 18 is a plot of a relationship between the focus position and theCD for each exposure dose.

DESCRIPTION OF THE EMBODIMENTS

Embodiments of the present invention will now be described in detail inaccordance with the accompanying drawings.

Referring now to FIG. 1, a description will be given of a semiconductormanufacturing system. The semiconductor manufacturing system includesplural exposure apparatuses (1 and 2 in FIG. 1), a shape measurementapparatus 3, a central processing apparatus 4 serves as a computer, adatabase 5, which are connected by a LAN 6, such as an in-house LAN.

The exposure apparatuses 1 and 2 are scanning exposure apparatuses, eachof which exposes a circuit of a reticle 20 onto a wafer 40 in astep-and-scan manner.

The shape measurement apparatus 3 obtains three-dimensional shapeinformation of a pattern formed on a substrate using the exposureapparatus that exposes the substrate via the original and uses a CD-SEM.The central processing apparatus 4 calculates a shift amount between theCD contained in the shape information and the reference value of the CDbased on the pattern's three-dimensional shape information, andcalculates the offsets of the exposure dose and the focus position.Here, the offset of the exposure dose is a gap from the optimal (target)exposure dose when target pattern is formed on the wafer. It is similarabout the focus position. The focus position is the position of thesubstrate in exposed areas. The focus position is represented by aposition in the optical-axis direction of the projection optical system.The database 5 forms a database and stores data, such as variousmeasurement values from the exposure apparatuses 1 and 2, and the shapemeasurement apparatus 3. The central processing apparatus 4 optimizesthe exposure dose and the focus position, and informs the exposureapparatuses 1 and 2 of the optimized ones.

Referring now to FIG. 2, a description will be given of the exposureapparatus 1.

The exposure apparatus 1 is a scanning exposure apparatus that exposes acircuit pattern of a reticle 20 onto a wafer 40 in a step-and-scanmanner. The exposure apparatus 1 includes, as shown in FIG. 2, anillumination apparatus 10, a reticle stage 25 that supports the reticle20, a projection optical system 30, a wafer stage 45 that supports thewafer 40, a focus/tilt detection system 50, and a controller 60. Thecontroller 60 has a CPU and a memory, is electrically connected to theillumination apparatus 10, the reticle stage 25, the wafer stage 45, andthe focus/tilt detection system 50, and controls the operation of theexposure apparatus 1. The controller 60 in this embodiment operates andcontrols so as to optimally set the wavelength of the light used for thefocus/tilt detection system 50 to detect a surface position of the wafer40. The exposure apparatus 1 of this embodiment uses the step-and-scanmanner, but the present invention is applicable to a step-and-repeatmanner.

The illumination apparatus 10 includes a light source 12 and anillumination optical system 14, and illuminates the reticle 20 that hasa circuit pattern to be transferred.

The light source 12 can use an ArF excimer laser with a wavelength ofapproximately 193 nm, but the light source may use a KrF excimer laserhaving a wavelength of about 248 nm, an F₂ laser with a wavelength ofapproximately 157 nm, an Extreme Ultraviolet (“EUV”) light source, and amercury lamp having a wavelength of 365 nm.

The illumination optical system 14 is an optical system that illuminatesthe reticle (mask) 20 that serves as an original, which is arranged on atarget plane to be illuminated, using the light from the light source12. The illumination optical system 14 includes a lens, a mirror, anoptical integrator, a stop, etc. The illumination optical system 14 canuse both axial and off-axial lights. The optical integrator is a fly-eyelens, but may use two sets of cylindrical arrays, an optical rod, and adiffraction optical system.

The reticle 20 is made, for example, of quartz, and has a circuitpattern to be transferred. The reticle 20 is supported and driven by thereticle stage 25. The exposure apparatus 1 includes a reticle detector70 of an obliquely light introducing system that detects a position ofthe reticle 20 so as to arrange the reticle 20 in place.

The reticle stage 25 supports the reticle 20 via a reticle chuck (notshown), and is connected to a moving mechanism (not shown). Theprojection optical system 30 projects the pattern of the reticle 20 ontothe wafer 40, and can use a dioptric optical system, a catadioptricoptical system or a catoptric optical system.

A photoresist is applied onto the wafer 40 that serves as a substrate.Instead of the wafer 40, another substrate, such as a liquid crystalsubstrate and a glass plate, may be used.

The wafer stage 45 supports the wafer 40 via a wafer chuck (not shown).

The focus/tilt detection system 50 includes, as shown in FIG. 2, anillumination part 52 that introduces the light to the wafer 40's surfaceat a high incident angle, a detector 54 that detects an image shift ofthe light reflected on the surface of the wafer 40, and an operatingpart. The illumination part 52 includes a light source, a lightsynthesizer, a patterned plate, an imaging lens, and a mirror. Thedetector 54 includes a mirror, a lens, an optical branching filter, anda light receiving unit.

The exposure apparatus 1 may serve as the shape measurement apparatus 3,the central processing apparatus 4, and the database 5 in thesemiconductor manufacturing system shown in FIG. 1. That embodiment canprovide the same operation and effect as those of the abovesemiconductor manufacturing system.

Referring now to FIG. 3, a description will be given of the exposuremethod 500 of this embodiment. Here, FIG. 3 is a flowchart of theexposure method 500.

The exposure method 500 exposes the substrate by calculating at leastthe offset of the focus position among the offsets of the exposure doseand the focus position in the exposure apparatus that exposes thesubstrate via the original.

The flowchart of the exposure method 500 is roughly classified intothree stages. The first stage includes the steps 501 to 504, correlatesthe exposure dose, the focus position, and the FEM pattern with pluralpieces of three-dimensional shape information obtained for each shot,and prepares a library in advance. More specifically, these stepsprepare an FEM wafer on which the FEM pattern is exposed, set theoptimal exposure condition (i.e., the exposure dose and the focusposition) utilizing the FEM wafer, and prepare the library through themultivariate analysis. The FEM pattern, as used herein, is a patternexposed in a matrix on the wafer having plural shots with parameters ofthe focus position and the exposure dose.

Based on the CD inspection result of the reticle pattern that isactually used in the mass-production stage, for a pattern having a largeCD error, the FEM pattern that uses the CD is also prepared. Nextfollows a correlation with plural pieces of three-dimensional shapeinformation. A library corresponding to the CD is then prepared.

The next stage includes the steps 505 to 507, and calculates the offsetsof the focus position and the exposure dose. These steps executeexposure with the reticle and wafer for the mass-production stage, andmeasure the resist pattern shape exposed on the wafer. Next follows averification with the library corresponding to the reticle's CD, and theoffsets of the focus position and the exposure dose from the optimalexposure condition are calculated.

Finally, the calculated offset data is sent to the exposure apparatus 1,and the exposure dose and the focus position are re-optimized (step508). In the mass-production stage, wafers are exposed under there-optimized exposure condition (step 509).

Next follows a detailed description of each step.

First, CD inspection data of a reticle used for the mass-productionstage is acquired (step 501). This embodiment prepares the reticle, andthen measures the CD of an actual device pattern at plural points on thereticle. However, even when the CD measurement value falls within themanufacture latitude, if the optimal exposure dose and focus positiondiffer after the pattern is transferred onto the wafer, developed, andetched, the pattern is regarded as a pattern for which a difference ofthe CD value should be considered. A location of the pattern on thereticle for which the difference should be considered, and a classifyingCD value are determined from the reticle's CD inspection data obtainedin the step 501.

Next follows a preparation of the FEM wafer (that has the FEM pattern)to the pattern for which the CD value difference should be considered asa result of the step 501 (step 502). The wafer may be a wafer actuallyused for the mass-production stage, or a test wafer configured similarto the wafer. A pattern forming range may be limited to a fine rangehaving only part of the pattern for which the CD value difference shouldbe considered, reducing the influence of flatness errors of the waferand reticle to be used.

FIG. 4 shows a flow from the exposure to the development of the FEMpattern, and is a flowchart of the FEM pattern manufacturing method inthe step 502.

Initially, the resist is applied onto the wafer, and a BARC and TARC areapplied as necessity arises (step 601). The resist applied wafer ispre-baked to stabilize the resist characteristic (step 602). Next, thewafer is fed to the exposure apparatus, and the image of the FEM patternis exposed on the wafer (step 603). Next, the wafer undergoes the postexposure bake (“PEB”) (step 604) and the development (step 605), and theFEM pattern is formed on the FEM wafer.

Next, shape information of the FEM pattern formed on the wafer isobtained with a stereo SEM or CD-AFM (step 503). FIGS. 5, 6 and 7 showactual measurement results with the stereo SEM. Here, FIG. 5 shows animage when the formed pattern is observed from the top of the wafer orin the height direction. FIG. 6 shows an image when the wafer on whichthe FEM pattern is formed is inclined by 15°. FIG. 7 is a graph of thepattern shape based on the image shown in FIG. 6.

FIG. 5 provides only a certain CD of the pattern, whereas pluralmeasurement values that serve as pattern's shape information areavailable from the data of FIG. 7, such as a sidewall angle and a heightin addition to the CD. Thereby, the pattern's three-dimensional shapecan be measured.

The FEM pattern shown in FIG. 8 is exposure results of plural shotswhile the focus position and the exposure dose are varied. The ordinateaxis denotes the focus position, and the abscissa axis denotes theexposure dose. Here, FIG. 8 is an enlarged view of the part of thepattern section in each shot of the FEM pattern formed on the wafer.FIG. 9 shows a measurement result illustration of CDs, such as tcd, mcd,and bcd, a height, and a sidewall angle (“swa”) that represent pattern'sshape information of the FEM pattern shown in FIG. 8 in each shot. FIG.9 correlates the pattern's shape information (tcd, mcd, bcd, height, andswa) in each shot of the FEM pattern with the focus position and theexposure dose used to expose the FEM wafer. Here, “tcd”is a CD near thetopside of the pattern. “bcd” is a CD near the downside of the pattern.“mcd” is a CD near a midpoint between the top and bottom sides of thepattern. The height and the sidewall angle are defined as shown in FIG.8. The focus position is represented by a distance from the referenceposition that is set to the origin.

The optimal focus position and exposure dose are determined from arelationship between the shape information and the exposure condition(i.e., the focus position and the exposure dose). For example, thepattern enclosed in the thick frame in FIG. 8 is closest to the targetpattern, and the focus position and exposure dose used to form thispattern become optimal and target values of the offsets. The optimalfocus position and the optimal exposure dose are the center values of aso-called ED window that is an area defined as the desired CD added tothe latitude. The latitude or permissible value is often ±10% of the CD.The reference value of the CD is a CD of the pattern, such as mcd, inthe thick frame shown in FIG. 8.

Next follows a preparation of libraries corresponding to the exposuredose and the focus position using plural pieces of shape informationobtained in step 503 through the multivariate analysis technique (step504). A detailed description will now be given of a production of thelibrary of the step 504.

A description will now be given of the manufacturing method of thelibrary used to calculate the offset of the exposure dose. A relationalequation representing a relationship between the exposure dose and theCD, such as mcd, will be created from the shape information (see FIG. 9)of the FEM pattern formed on the FEM wafer. The relationship isformulized between the exposure dose and the CD variance of the pluralpatterns enclosed by the thick frame of the FEM pattern shown in FIG.10. Here, similar to FIG. 8, FIG. 10 is an enlarged view of part of thepattern section in each shot of the FEM pattern formed on the wafer.FIG. 11 is a graph of a relationship between the CD and the exposuredose obtained from plural patterns in the thick frame in FIG. 10, andthe relationship between the exposure dose and the CD is obtainedthrough a polynomial approximation. The approximated equation isexpressed by Equation 1 below, where f₁ is a function:(Exposure Dose)=f ₁ (Critical Dimension)  EQUATION 1

The storage of the central processing apparatus 4 or the database 5shown in FIG. 1 stores this approximated equation as a relationalequation of a first library used to calculate the offset from theoptimal exposure dose value.

The relationship between the CD variance amount and the exposure dosevariance amount expressed by Equation 1 is invariable with the extrinsicfactor, such as the resist's refractive index and thickness, exposurecontrol and focusing of the exposure apparatus, a development timeperiod, a developer's characteristic, an uneven hot plate, a PEBtemperature and time period, and a reticle manufacturing error(flatness).

Next, a relationship is formulized between the CD and the focus positioncalculated from the plural patterns in the thick frame of the FEMpattern shown in FIG. 12. FIG. 13 is a graph of a relationship betweenthe CD and the focus position obtained from the plural patterns shown inFIG. 12, and the relationship between them is obtained through thepolynomial approximation. The polynomial approximation is expressed byEquation 2 below, where f₂ is a function:(Critical Dimension)=f ₂ (Focus Position)  EQUATION 2

The storage of the central processing apparatus 4 or the database 5stores this approximated equation as a relational equation of a secondlibrary used to calculate the offset from the optimal exposure dosevalue.

Similar to Equation 1, a relationship between the CD variance amount andthe exposure dose variance amount expressed by Equation 1 is invariablewith the above extrinsic factor.

Finally, a third library is defined as a relational equation among theCD (X), height (Y), and sidewall (Z) of the FEM pattern, and the focusposition. When this equation is approximated by the N-th orderpolynomial, it is generally expressed by Equation 3. N is an integerused to calculate the orders of the CD, height and sidewall of the FEMpattern. f₃ is a function, and al to aN, b1 to bN, cl to cN, and d0 areconstants.(Focus Position)=f ₃ (CD, height, sidewall)=a ₁ X+a ₂ X ² +. . . +a _(N)X ^(N+) b ₁ Y+b ₂ Y ² + . . . +b _(N) Y ^(N) +c ₁ Z+c ₂ Z ² + . . . +c_(N) Z ^(N) +d ₀  EQUATION 3

The storage of the central processing apparatus 4 or the database 5stores this approximated equation as a third library.

Equation 3 is a function using the CD, height, and sidewall of the FEMpattern for variables to calculate the focus position. However, thevariables to be used are not limited to this embodiment, and mayadditionally use the exposure dose calculated by Equation 1 in additionto the CD, height, and sidewall of the FEM pattern.

Similar to Equations 1 and 2, the above relationship expressed byEquation 3 is invariable with the above extrinsic factor.

The relationships expressed by the above three equations do not dependupon the extrinsic factor, or no libraries expressed by these equationsrequire an update due to the extrinsic factor. On the other hand,Japanese Patent Application, Publication No. 2003-142397 does not usethese equations, and needs to update the library in accordance with theextrinsic factor.

In preparing the library, the FEM pattern is also prepared for a patternhaving a large CD error based on the reticle pattern actually used forthe mass production, and correlated with plural pieces of pattern shapeinformation, and a library corresponding to the CD is additionallyprepared.

The steps 501 to 504 shown in FIG. 1 for previously preparing thelibrary are thus described.

A description will now be given of a sequence of the steps 505 to 508used to calculate the offsets of the focus position and the exposuredose.

Initially, the entire shot on the wafer is exposed and developed similarto the mass-production stage using the reticle, wafer, and the exposureapparatus, which are used for the actual mass-production stage (step505). The exposure condition at this time may use the center of the EDwindow calculated in the step 503.

Next, shape information of a pattern formed on the wafer by using theexposure apparatus is obtained (step 506). Similar to the step 503, thestereo SEM or CD-AFM is used to obtain plural pieces of shapeinformation, such as a CD, height, and sidewall angle.

Next, the offset of the exposure dose and the offset of the focusposition are calculated using the plural pieces of shape informationobtained in the step 506 (step 507).

First, the offset of the exposure dose is calculated from the optimalexposure dose using the first library, creating a provisional exposuredose offset. Next, the offset of the focus position from the optimalfocus position is calculated using the third library. A shift amountfrom the reference value of one value among the plural pieces of shapeinformation is calculated based on the offset from the optimal focusposition and the second library. An exposure dose to be corrected isobtained from this value using the first library, and added to theprovisional exposure dose offset that has been obtained, creating theoffset of the exposure dose.

More specifically, a description will be given with reference to FIGS.14, 15 and 18. Here, FIG. 14 is a graph showing the offsets from theoptimal focus position and the optimal exposure dose, which arecalculated from FIG. 8. FIG. 15 is a flowchart for calculating theoffset of the focus position and the offset of the exposure dose usingthe shape information of the measured FEM pattern. FIG. 18 is a plot ofa relationship among the focus position, mcd, and the exposure dose.

In the FEM pattern shown in FIG. 14, the sectional shape 1 is a shapeexposed under the optimal exposure condition (i.e., the exposure doseand focus position). The sectional shape 2 is a shape exposed in thestep 505. The exposure dose and the focus position shift from theoptimal exposure condition, as shown in FIG. 14. P4 in FIG. 18 denotes apattern shape having the sectional shape 1. P1 in FIG. 18 corresponds tothe sectional shape 2.

In FIG. 15, the first library stored in the memory in step 504 and aninput value of a difference between the reference value and one ofplural pieces of pattern's shape information are used to calculate theoffset Δdose 1 of the first exposure dose (step 701). More specifically,the offset Δdose 1 is calculated from a difference between one of theplural pieces of shape information indicative of the sectional shape 2in FIG. 14, such as mcd, one of the plural pieces of shape informationindicated by the sectional shape 1 of the optimal exposure condition(the reference value of mcd). Δdose 1 is a difference between dose 4 anddose 2, as shown in FIG. 18. When P1 shifts by Δdose 1, a position of P2is obtained.

Next, the focus position is obtained with the above third library andinput measurement values of plural pieces of shape information. Adifference between the focus position and the optimal focus position isobtained as an offset Δfocus of the focus position (step 702). FIG. 18shows Δfocus.

Next, the offset Δdose 2 of a second exposure dose is calculated in FIG.15 (step 703). Δdose 2 is a necessary correction amount of the exposuredose to correct a CD shift of the resist pattern that newly occurs whenthe focus position is corrected by calculated Δfocus. A position of P3is obtained when P2 shifts by Δfocus with dose 2 as shown in FIG. 18,and it is understood that the CD shift occurs.

Δdose 2 can be calculated by substituting Δfocus for the second libraryrelating to the exposure dose obtained in the step 504, by calculatingthe CD shift amount ΔCD, and by substituting ΔCD for the first library.When P3 shifts by Δdose 2, as shown in FIG. 18, a position of P4 isobtained, and Δdose 2 is a difference between dose 1 and dose 2.Finally, the exposure dose offset Δdose of the resist pattern iscalculated as Δdose=Δdose 1+Δdose 2 (step 704).

A location the CD size difference is discernable on the actual reticlebased on the reticle inspection data obtained in the step 501.Therefore, the offsets from the optimal exposure condition, i.e., thefocus position and the exposure dose, are calculated using the libraryin accordance with the reticle inspection data.

The offsets of the focus position and the exposure dose are thuscalculated through steps 505 to 507 shown in FIG. 3.

Finally, the offset Δdose of the exposure dose, the offset Δfocus of thefocus position, which are thus obtained in the above procedure, are fedback to the exposure apparatus, or fed forward (step 508). Then, thewafer 40 is exposed with the optimized exposure condition in themass-production stage (step 509), and the resist pattern that is exposedunder the optimal exposure condition becomes a target shape.

This embodiment uses only one value, such as mcd, among the plural shapemeasurement values for the library necessary to correct the exposuredose, but can use other solid shape information. In addition, thisembodiment uses a linear or quadratic approximated equation for theapproximated equation used to calculate the exposure dose, but can usecubic or higher approximated equation.

When the exposure apparatus is a scanner, the exposure region has a slitshape. When the step 506 shown in FIG. 3 measures shapes in plural areascorresponding to plural points in the slit, the offset of the focusposition is determined by a plane for controlling a least squareapproximation plane of the offset of the focus in plural areas, and theexposure may be performed while the focus position and the tilt amountare varied.

For example, when the aberration of the projection optical system isvariable in the exposure apparatus, and accords with the surface shapeof the offset of the focus position at plural points, the exposure maybe provided, for example, by changing the aberration of the projectionoptical system and the plane of the even function that becomes acurvature of field, rather than a least squares approximation plane.

With respect to the exposure dose, the optimal value may differaccording to shots on the wafer, or an optimal exposure dose may be setat different positions in each shot. The offset amount of the exposuredose may be set at each position in the slit-shaped exposure region.Even when the offset of the exposure dose is set in the reticle orwafer's scanning direction, a slit width of the illumination opticalsystem may be made variable, or another measure may be made.

Thus, when the pattern's shape information is obtained for each ofplural areas on the wafer, the optimal offsets of the exposure dose andthe focus position can be calculated for the entire device.

As discussed above, this exposure method 500 does not expose, in themass-production stage, unlike the FEM, by minutely changing a focusposition, but sets the optimal offsets of the exposure dose and focusposition by considering the error due to the extrinsic factor from oneexposure condition. Therefore, even when the extrinsic factor thataffects the CD fluctuates, the library does not have to be updated. As aresult, the exposure method 500 can process the wafer at a highthroughput, and inexpensively provide liquid crystal and other devices.In addition, the operation processing described above is performed as acomputer program using the central processing apparatus 4, the offset ofthe exposure dose and the focus position are calculated.

A description will now be given of a semiconductor device manufacturingprocess using the above exposure method. FIG. 16 is a flowchart forexplaining a fabrication of devices. Here, a description will be givenof a fabrication of a semiconductor device as an example. Step 1(circuit design) designs a semiconductor device circuit. Step 2 (reticlefabrication) forms a reticle having a designed circuit pattern. Step 3(wafer preparation) manufactures a wafer using materials such assilicon. Step 4 (wafer process), which is referred to as a pretreatment,forms actual circuitry on the wafer through photolithography using thereticle and wafer. Step 5 (assembly), which is also referred to as apost-treatment, forms into a semiconductor chip the wafer formed in Step4 and includes an assembly step (e.g., dicing, bonding), a packagingstep (chip sealing), and the like. Step 6 (inspection) performs varioustests for the semiconductor device made in Step 5, such as a validitytest and a durability test. Through these steps, a semiconductor deviceis finished and shipped (Step 7).

FIG. 17 is a detailed flowchart of the wafer process. Step 11(oxidation) oxidizes the wafer's surface. Step 12 (CVD) forms aninsulating film on the wafer's surface. Step 13 (electrode formation)forms electrodes on the wafer by vapor disposition and the like. Step 14(ion implantation) implants ions into the wafer. Step 15 (resistprocess) applies a photosensitive material onto the wafer. Step 16(exposure) uses the above exposure method to expose a reticle patternonto the wafer. Step 17 (development) develops the exposed wafer. Step18 (etching) etches parts other than a developed resist image. Step 19(resist stripping) removes disused resist after etching. These steps arerepeated, and multilayer circuit patterns are formed on the wafer.

The entire disclosure of Japanese Patent Applications Nos. 2006-000950,filed on Jan. 5, 2006 and 2006-353324, filed on Dec. 27, 2006, includingclaims, specification, drawings, and abstract incorporated herein byreference in its entirety.

As many apparently widely different embodiments of the present inventioncan be made without departing from the sprit and scope thereof, it is tobe understood that the invention is not limited to the specificembodiments thereof except as defined in the claims.

1. A method for calculating an offset of an exposure dose and a focusposition in an exposure apparatus that exposes a substrate via anoriginal, said method comprising: a first step of obtaining informationof a shape of a pattern formed on the substrate using the exposureapparatus; a second step of calculating a shift amount between acritical dimension contained in the information of the shape of thepattern and a reference value of the critical dimension; and a thirdstep of calculating an offset of the focus position based on theinformation of the shape of the pattern, and calculating the offset ofthe exposure dose based on the shift amount and the offset of the focusposition.
 2. A method according to claim 1, wherein the third steppreviously calculates a first library indicative of a relationshipbetween the exposure dose and the critical dimension, a second libraryindicative of a relationship between the critical dimension and thefocus position, and a third library indicative of the focus position andthe information of the shape of the pattern, the third step calculatingthe offset of the focus position using the third library and calculatingthe offset of the exposure dose using the first, second, libraries andthe focus position.
 3. A method according to claim 1, wherein the firststep obtains the information of the shape of the pattern for each ofplural areas on the substrate.
 4. A method according to claim 3, whereinthe third step calculates the offset of the exposure dose and the offsetof the focus position for each of plural areas on the substrate.
 5. Anexposure method for exposing a substrate based on an offset of anexposure dose and an offset of the focus position calculated by a methodaccording to claim
 1. 6. A program for enabling a computer to execute amethod for calculating an offset of an exposure dose and a focusposition in an exposure apparatus that exposes a substrate via anoriginal, said method comprising: a first step of obtaining informationof a shape of a pattern formed on the substrate using the exposureapparatus; a second step of calculating a shift amount between acritical dimension contained in the information of the shape of thepattern and a reference value of the critical dimension; and a thirdstep of calculating an offset of the focus position based on theinformation of the shape of the pattern, and calculating the offset ofthe exposure dose based on the shift amount and the offset of the focusposition.
 7. A program according to claim 6, wherein the third steppreviously calculates a first library indicative of a relationshipbetween the exposure dose and the critical dimension, a second libraryindicative of a relationship between the critical dimension and thefocus position, and a third library indicative of the focus position andthe information of the shape of the pattern, the third step calculatingthe offset of the focus position using the third library and calculatingthe offset of the exposure dose using the first, second libraries andthe offset of the focus position.
 8. A device manufacturing methodcomprising the steps of: exposing a substrate using an exposure methodaccording to claim 5; and developing the substrate that has beenexposed.
 9. A method for calculating a focus position in an exposureapparatus that exposes a substrate via an original, said methodcomprising: a first step of obtaining information of a shape of apattern formed on the substrate using the exposure apparatus; a secondstep of calculating a shift amount between a critical dimensioncontained in the information of the shape of the pattern and a referencevalue of the critical dimension; and a third step of calculating anoffset of the focus position based on the information of the shape ofthe pattern.